Material science defines the structural properties of an object as the properties that describe the object's makeup independent from its shape. The structural properties of adult human bone are complex and can be modeled as a four-order hierarchy, arranged in decreasing size (Petersen, 1930). The first order, macrostructure, comprises the structures corresponding to gross shape and differentiation between compact (or cortical) bone and spongy (cancellous or trabecular) bone. Compact bone is present in the long bone shaft (or diaphysis). Spongy bone is present in the lower jaw (mandible), in the epiphysis of long bone shaft, and in flat and short bones. The second order (or microstructure) includes lamellar systems (lamellae) and related structures such as bone marrow (see, e.g., Bloom and Fawcetts, 1986). In compact bone, organized lamellae around vascular (harvesian) canals are referred to as secondary osteons (harvesian systems), and portions of osteons among whole osteons are referred to as the interstitial bone. For cancellous bone, the second order consists of lamellar systems that form trabeculae. The third order (or ultrastructure) of both compact and cancellous bone consists of the organic phase (mainly of type 1 collagen) and the inorganic phase (carbonated apatite crystallites); mucopolysaccarides amount to a small amount but may have a significant role. The apatite crystallites are oriented locally along the collagen fibril orientation. The fourth order of compact bone consists of molecular arrangements between organic and inorganic substances.
At the microstructural level, the osteon comprises a haversian canal with coaxially arranged lamellae. Osteons measure a few centimeters in length, and between 150 and 300 μm in diameter. The osteon axis is generally oriented along the axis of the long bone to which it belongs. The degree of osteon calcification (relative amount of apatite crystallites) is variable from osteon to osteon as well as within osteons. These differences are proposed to be due to the continuous process of bone renewal, or remodeling, that osteons undergo. Consequently, osteons at different degrees of calcification are always present in adult compact bone.
Two lamellar types exist: the one that appears essentially extinct and the one that appear bright under circularly polarized light. Extinct lamellae consist of collagen fibrils with a marked longitudinal spiral course. Bright lamellae consist of collagen fibrils with a marked oblique and transversal course in successive lamellae (Frasca et al., 1977, Giraud-Guille, 1988, Ascenzi M.-G. et al., 2003). The arrangement of lamellae within the osteon produces a spectrum of osteon types by their appearance under circularly polarized light.
The trabeculae of cancellous bone are osseous structures with either a sheet-like or a rod-like configuration. These structures interlace to form a lattice-like or spongy biological structure. For example, both types of trabeculae are present in the calcaneous; however, up to 3% of the rod-like configurations are tubular due to the vascular canal running through them. Therefore, they are similar to the harvesian system. In general, tubular trabeculae appear to have a relatively simple structure. Collagen fibrils run mostly parallel to the long axis of tubular trabeculae in the trabeculae outer portion and perpendicular in the inner portion.
Compact bone consists of about 40% minerals, 40% collagen, and 20% fluids. The major internal spaces or discontinuities of compact bone include the vascular system, pits and cavities (lacunae), narrow channels (canaliculae), fine porosity, and spaces between the mineral phases. The major internal material discontinuities of compact bone, in order of decreasing size, are:
Vascular system20-50□mLacunae4-6□mCanaliculae0.5-2□mFine porosity600-800ÅSpaces between mineral phases50-100Å
Although the true density of fully calcified cancellous bone is a little lower and the proteoglycan content a little greater than those of the fully calcified compact bone, the substantial difference between compact and cancellous bone resides in the porosity. The cancellous bone porosity, which ranges from 30% to more than 90%, is mainly due to the wide vascular and bone marrow intrabecular spaces. As is seen in compact bone, levels of calcification vary from trabecula to trabecula and within trabeculae.
The connections and orientations of trabeculae are found to have precise patterns, which are believed to relate to specific mechanical properties. The structure of the cancellous bone in the head and in the neck of the femur is usually given as an example of the correlation between the orientation of the trabeculae and the linear distribution of the principal forces during load bearing (stress trajectoral theory (Bell, 1956)). In general, such correlation between the orientation of the trabeculae and the linear distribution of the principal forces during load bearing is still under study because while in line with the mathematical calculations, the possible effect of muscle traction is complex (Koch, 1917; Rybicki et al., 1972). Nevertheless, there is a close relationship between the number and arrangement of trabeculae and the strength of cancellous bone (see, e.g., Kleerekoper et al., 1985). This is evidenced by the age-induced loss of trabeculae (see, e.g., Birkenhäger-Frenkel et al., 1988). Since this loss is rather selective (i.e. transverse trabeculae disappear more frequently than vertical ones in the central zone of the osteoporotic vertebral body; entire trabeculae totally disappear in elderly women; sharp fall in trabecular number is seen in elderly men), it is possible that cancellous bone contains some bundles of trabeculae whose main function is to resist mechanical forces while others have mainly a metabolic role.
The mechanical behavior of a material, or the response of the material to forces, depends on the structure of the material. If the material consists of a hierarchical structure, the mechanical behavior of the material depends on the contributions of the hierarchical levels. Each level or order of the hierarchy responds to the forces according to the substructures within that order and relationships with the orders of which it is a sublevel. Further, patterns of lower hierarchical levels at higher hierarchical levels may play a relevant role in the mechanical properties of the higher level. Therefore, the mechanical properties of a material will depend on the hierarchical level of the material. Bone is an example of a material where the mechanical behavior and mechanical properties are dependent upon this kind of multilevel structure.
Mechanical properties of bone have been and are being investigated at various hierarchical levels through invasive (specimen isolation) and non-invasive testing. Osteonic lamellae, osteons, trabeculae, and macroscopic compact and cancellous bone samples have been and are the objects of such studies. Micromechanical results include Ascenzi A. and Bonucci, 1964, 1967; Ascenzi A. and Bonucci, 1968, 1972; Currey, 1969; Ascenzi A. et al., 1985, 1997, 1998; Hohling et al., 1990; Ascenzi A. et al., 1990, 1994; Marotti et al., 1994; Ziv et al., 1996; Ascenzi M.-G., 1999, 1999a; Huja et al., 1999; Zysset et al., 1999; Ascenzi M.-G. et al., 2000. Macromechanical results include Hazama, 1956; Cook and Gordon, 1964; Carter and Hayes, 1976 and 1977; Carter et al., 1976 and 1981; Carter and Spengler, 1978; Hayes and Carter, 1979; Burr et al., 1988; Cater and Carter 1989; Jepsen and Davy, 1997.
Many investigators have devoted their research to model the structure of secondary osteons either in the context of the macrostructure (see, e.g., Katz, 1981; Hogan, 1992; Aoubiza et al., 1996) or as a self-contained structure (Akiva et al., 1998; Ascenzi M.-G., 1999, Weiner et al., 1999, Jäger and Fratzl, 2000, Kothawz and Guzelsu, 2002; Gotha and Guzelsu, 2002; and Ascenzi M.-G. et al., 2003 and 2004). The work of these investigators includes development of mechanical theories and application of finite element and analytical methods based on and verified by experiments, as discussed in more detail below.
Following Leeuwenhoek's early observations (1693), the lamellar structure of secondary osteons in human bone has remained the subject of numerous investigations. While researchers over the centuries have agreed on the existence of two lamellar types, different hypotheses as to the structural characteristics that differentiate one type from the other were presented. The debate focused principally on the organization of collagen fibrils and carbonated apatite crystallites, the main elementary components of secondary osteons.
The differences of opinion were sustained by the challenges: (1) to optimize microscopy technique and specimen preparation for structural visualization of lamellae whose thickness ranges between a mere 2 and 16 microns and whose shape is curved; (2) to interpret the microscopy observation of structure in terms of orientation and density of collagen and apatite; and (3) to extrapolate the 3-dimensional biological reality of macroscopic bone from the 2-dimensional information provided by the microscopy plane of focus on specimens excised from macroscopic bone at specific orientations and observed at specific angles.
To confront these challenges, investigators employed increasingly sophisticated microscopy tools with higher magnifications and resolutions as they became available. These tools have enabled acquisition of knowledge about the lamellar structure and provided the foundation for further refined structural hypotheses. Further, the development of materials science and engineering theories over time has allowed more robust testing and assessment of the hypotheses formulated by the various investigators. In recent decades, increasing computer capability and software sophistication have allowed simulation of mechanical testing of lamellae and osteons to include greater structural detail so as to explain function with higher accuracy.
The following is a review of early compound microscopy investigations of lamellar structure, modern microscopy investigations, and previous lamellar modeling to provide context for the present invention.
The earliest microscope of the 1590's was merely a tube with a plate for the object at one end, and at the other, a lens which yielded a magnification of less than ten times actual size. Leeuwenhoek devised techniques to grind and polish small lenses of great curvature that afforded his microscopes unprecedented 270× magnification. His examination of bone revealed osteons and their lamellae (Leeuwenhoek, 1693). Microscopes of the time used light to illuminate the bone specimen, and their magnifications were not bettered by more than an order of magnitude until the twentieth century. The limitation on magnification was the wavelength of light. With white light, any two details closer than 0.275 micrometers are seen as a single detail by an ordinary light microscope, and any detail with a diameter smaller than 0.275 micrometers will be either invisible or blurry. Over time, the magnification available by compound microscopes became only approximately an order of magnitude higher, up to 1800× with ordinary light and up to 5000× with blue light.
Kölliker (1854), by regular light microscopy with magnifications up to 350×, perceived “lamellated” bone matrix with two layers in each lamella: one layer as pale and more homogeneous; a second layer as darker, granular and for the most part striated. He hypothesized that differences in elementary component densities might explain the difference in appearance. Ebner (1875) was one of the first researchers to employ polarization of light in a compound microscope for lamellar investigations. When light is forced to travel as a plane wave through a bone specimen placed between a so-called polarizer and a so-called analyzer, the image seen through the eye pieces of the microscope consists of either extinct or bright signals depending on whether the light passes through the specimen substructures. That the concentric lamellae of an osteon in cross-section gives rise to either an extinct or bright polarized light signal points to a difference in the structure of the underlying lamellae. However, the significance of the signal requires interpretation because the extinct or bright signal per se does not yield information about the structural differences that determine its appearance. By means of a magnification up to 600× under polarized light, Ebner interpreted the appearance of “lamellation” as due to orientation of “connective fibers”. He hypothesized that the “connective fibers” were a component of bone tissue, separate from calcium salts that would lie in the spaces between the fibers.
Ranvier (1887) followed Kölliker's terminology of differentiation between homogeneous lamella and streaked lamella. At a magnification up to 600× under polarized light, he associated an extinct appearance to the streaked lamella and a bright appearance to the homogeneous lamella. He hypothesized that the different extinct or bright appearance is due to a difference of fiber orientation. Because fibers viewed transversely to their axis appear extinct, the homogenous lamella would appear extinct on a section transverse to the osteon axis by virtue of its fibers being viewed transversely to their axis. Because fibers viewed along their length appear bright, the streaked lamella would appear bright on a section transverse to the osteon axis by virtue of its fibers being viewed along their axis. This association of the polarization signal with fiber orientation was at that time a non-verified hypothesis derived through reasoning on the physics of the polarized light microscopy. Gebhardt (1906) also interpreted the differences in lamellar types, viewed through regular and polarized light microscopy, in terms of orientation of higher percentage components. More specifically he proposed what in modern terminology is defined as an orthogonal or quasi-orthogonal plywood osteonic model, where collagen fibrils change orientation from a lamella to the next one. Ziegler (1906) instead interpreted the different appearance of lamellae under polarized light as resulting from a difference in density associated with fibrillar lamellae separated by what he defined as interstitial substance, without fibrillae extending from a lamella to the next.
Weidenreich (1930) conducted his regular light microscopy investigations with up to 1040× magnification and supported Gebhardt's interpretation of difference as due to orientation of elementary components. Ruth (1947), through regular light microscopy of up to 1800× magnification differentiated between compact and diffuse lamellae in accordance with their structural appearance. He saw “compact lamellae” as bands of circumferentially oriented compact, felted or interwoven bundles of fibrillae, and “diffuse lamellae” as bands of radially oriented fibrillae, loosely disposed, and separated from each other by relatively wide interfibrillar spaces filled with a granular substance. The fibrillae themselves were observed as delicate strands disposed at right angles to the compact lamellae.
Amprino (1946) and Amprino and Engström (1952) addressed the issue of developing a technique to investigate carbonated apatite density. They developed a high-resolution micro-X-ray that showed variation of degree of calcification among secondary osteons. Engström and Engfeldt (1953) showed that X-ray absorption varies in lamellae. They hypothesized existence of lamellae with a high content of organic and inorganic material alternating with lamellae containing less substance.
The application in the 1950's of transmission electron microscopy to secondary osteons, some twenty years following its invention, offered a new level of insight. In this kind of microscope, electrons are accelerated in a vacuum until their wavelength is extremely short, only one hundred-thousandth that of white light. Beams of these fast-moving electrons are focused on a specimen and are absorbed or scattered by the specimen so as to form an image on an electron-sensitive viewing screen. Electron microscopy allows magnification of objects up to 1 million times and a resolution up to 10 Å. Because initially the tools to cut ultra-thin bone sections suitable for transmission electron microscopy were not available, resin was employed to prepare a surface replica of the bone specimen. The replica, instead of the bone, was then observed with the electron microscope. The scanning electron microscope, which differs from the transmission electron microscope in that it detects secondary electrons emitted from the specimen surface after excitation by a primary electron beam instead of detecting electrons that pass through the specimen, was invented later and employed on bone, as discussed below, starting in the 1980s.
Rouiller et al. (1952) using regular light microscopy, polarized light and transmission electron microscopy, further substantiated Ruth's hypotheses. Frank (Frank et al., 1955; Frank, 1957) observed a variety of fibrillar orientation on osteon specimens cut at various orientations with respect to the Haversian canal by transmission electron microscopy. Vincent (1957) supported the density hypothesis by means of micro-X-ray and polarized light microscopy. Smith (1960) supported the orientation hypothesis and started a classification of osteon types based on micro-X-ray and electron microscopy observations.
Starting in the 1960's, Ascenzi A. and collaborators employed regular and polarized light microscopy as well as micro-X-ray (Ascenzi A. and Bonucci, 1961), electron microscopy (Ascenzi A. et al., 1966), and X-ray synchrotron diffraction (starting with Ascenzi A. et al., 1978) to observe bone micro- and ultra-structures. In particular, they established that the composition of bone specimens of dimensions even as small as 1 mm would vary greatly from specimen to specimen. In their micro-structural investigations they sought to address such variations so as to avoid large standard deviations of experimental data associated with variable, unknown compositions of specimen substructures. To address the composition variability, micro-specimens of specific appearance under polarized light and of fixed degree of calcification needed to be prepared so as to separate the variables and to appreciate their mechanical influence on the properties of bone tissue. Accordingly, Ascenzi A. and collaborators developed techniques for single osteon isolation and single lamellar isolation. They employed isolated single osteons and lamellae to show by mechanical testing that collagen-apatite orientation and degree of calcification are two independent variables (for a review, see Ascenzi M.-G. et al., 2000). To the previously available techniques, synchrotron diffraction added the detection of apatite crystallite orientation patterns and their level of organization through the thickness of isolated single osteons, osteonal hemisections, and isolated single lamellae. Their work (Ascenzi A. and Benvenuti, 1977; Ascenzi M.-G., 1999) extended to the observation of natural stress state differences between lamellar types. The Ascenzi group also found that the lamellar types, not the osteons, are the microstructures that form patterns within macro-structure and are ultimately responsible for giving rise to the combinations most suitable to withstand different stress conditions. Such findings apply to bone tissue under normal and pathological conditions (Ascenzi A., 1988).
Giraud-Guille (1988) established through transmitted electron microscopy the so-called rotated plywood model. A continuous rotation of fiber reinforcement from one layer to the next layer refines Gebhardt's model and explains the ability of the osteon to resist stresses directed along a larger range of orientations. Marotti and Muglia (1988) through scanning electron microscopy point to a difference between more or less loose lamellae in terms of collagen density. The “loose” lamella would contain perhaps a lower collagen density (still on the order of 90% of lamellar volume) and a higher content of non-collagenic protein which would give a more porotic appearance to the bone tissue and a more disordered orientation of collagen fibrils. Reid (1986) used scanning electron microscopy to indicate that lamellae that appear extinct under polarized light on a section transverse to the osteon axis consist of fibrils parallel to the osteon axis while lamellae that appear bright on a section transverse to the osteon axis consist of fibrils perpendicular to the osteon axis.
Structural models of secondary osteons, either in the context of the macrostructure or as a self-contained structure, have been created over time as information about bone structural and mechanical properties became increasingly available in conjunction with the development of engineering theories and increased computer capacity. Such models have addressed a variety of issues, including stress distribution in specimens under specific loading conditions, fracture propagation, and bone remodeling. The mechanical properties of the osteon, simplified to an extreme degree in initial models, were increasingly reflected with greater detail in more accurate models. Such models include development of mechanical theories that describe the microstructural behavior, as well as applications of finite element and analytical methods.
Galileo's observations on long bones of large mammals suggested the need for presence of micro-structures that would enhance the mechanical properties in the longitudinal direction of long bone shaft (Galilei, 1638). In this sense, Katz (1981) and Hogan (1992) viewed osteons as reinforcement to the macrostructure. Aoubiza et al. (1996) provided the first model of osteon groups with mechanical properties that depend on the collagen-apatite orientation within lamellae. Akiva et al. (1998) developed a mathematical model for each lamellar type that subdivides the lamella into volumes where the mineralized phase follows a specific orientation. The models of Weiner et al. (1997, 1999) support the hypothesis that most of the microstructural mechanical properties are built into the lamellar structure. Jäger and Fratzl (2000) proposed a mineralized collagen fibril model with a staggered, instead of parallel, arrangement of the mineral phase to better account for the increase in elastic modulus and fracture stress with increasing mineral content. Kotha and Guzelsu (2002) described through shear-lag theory debonding of matrix from mineral phase due to applied tensile loading in the direction of the apatite crystals. Ascenzi M.-G. (1999) assessed the prestress in isolated single lamellae that appear bright before isolation when still embedded in the surrounding osteons viewed in cross-section. Ascenzi M.-G. et al. (2004) established the methodology to create a virtual osteon from the experimentally observed biological variation of distribution of lamellae, osteocyte lacunae and canaliculae.
Ascenzi M.-G. et al. (2003) established the answer to Leeuwenhoek's query, that specific orientations of collagen fibrils and apatite crystals define and distinguish different human lamellar types. The novel combination of polarized light microscopy, synchrotron diffraction and confocal microscopy, applied to lamellar specimens isolated by a novel micro-dissection technique, evidenced that specific orientations of collagen fibrils and apatite crystals define and distinguish the appearance of lamellae under polarized light microscopy. That is, these combined techniques established that the presence of specific orientations determines whether the concentric lamellae of an osteon transverse section under circularly polarized light appear extinct or bright. As an illustration, FIG. 1a shows a so-called alternate osteon, an osteon in which lamellae appear alternatively extinct and bright in a circularly polarized light image. The micro-dissection technique which Ascenzi M.-G. et al. (2003) applied to alternate osteons allowed isolation of single lamellar specimens viewable by confocal microscopy through the lamellar thickness direction, which corresponds to the radial direction of the embedded osteon prior to the isolation of the specimen.